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原始二阶 ODE 是

x'' - 2 * omega * y' - omega ** 2 * x = - mue * (x + pi2 * r12) / np.sqrt((x + pi2 * r12) ** 2 + y ** 2) ** 3 - mum * (x - pi1 * r12) / np.sqrt((x - pi1 * r12) ** 2 + y ** 2)
y'' + 2 * omega * x' - omega **2 * y = - mue * y / np.sqrt((x + pi2 * r12) ** 2 + y ** 2) ** 3 - mum * y / np.sqrt((x - pi1 * r12) ** 2 + y ** 2)
z'' = 0

所以这是我用来解决 ODE 的代码，但首先我将它分成 2 个一阶。

我收到第 61 行的模块不可调用的错误。

第 61 行是u = odeint(deriv, u0, dt)

#!/usr/bin/env python                                                             

import numpy as np
import scipy.integrate as odeint
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

me = 5.974 * 10 ** (24)  #  mass of the earth                                     
mm = 7.348 * 10 ** (22)  #  mass of the moon                                      
G = 6.67259 * 10 ** (-20)  #  gravitational parameter                             
re = 6378.0  #  radius of the earth in km                                         
rm = 1737.0  #  radius of the moon in km                                          
r12 = 384400.0  #  distance between the CoM of the earth and moon                 
M = me + mm

pi1 = me / M
pi2 = mm / M
mue = 398600.0  #  gravitational parameter of earth km^3/sec^2                    
mum = G * mm  #  grav param of the moon                                           
mu = mue + mum
omega = np.sqrt(mu / r12 ** 3)
nu = 0.0  #  flight path angle                                                    

x = 327156.0  #  x location where the moon's SOI effects the spacecraft           
y = 33050.0   #  y location                                                       

vbo = 10.85  #  velocity at burnout                                               

gamma = -141.868 * np.pi / 180  #  angle in radians of true anomaly               

vx = vbo * (np.sin(gamma) * np.cos(nu) - np.cos(gamma) * np.sin(nu))
#  velocity of the bo in the x direction                                          
vy = vbo * (np.sin(gamma) * np.sin(nu) + np.cos(gamma) * np.cos(nu))
#  velocity of the bo in the y direction                                          

xrel = (re + 300.0) * np.cos(gamma)
#  spacecraft x location relative to the earth                                    
yrel = (re + 300.0) * np.sin(gamma)

#  r0 = [xrel, yrel, 0]                                                           
#  v0 = [vx, vy, 0]              
u0 = [xrel, yrel, 0, vx, vy, 0]


def deriv(u, dt):
    n1 = -((mue * (u[0] + pi2 * r12) / np.sqrt((u[0] + pi2 * r12) ** 2
                                               + u[1] ** 2) ** 3)
        - (mum * (u[0] - pi1 * r12) / np.sqrt((u[0] - pi1 * r12) ** 2
                                              + u[1] ** 2) ** 3))
    n2 = -((mue * u[1] / np.sqrt((u[0] + pi2 * r12) ** 2 + u[1] ** 2) ** 3)
        - (mum * u[1] / np.sqrt((u[0] - pi1 * r12) ** 2 + u[1] ** 2) ** 3))
    return [u[3],  #  dotu[0] = u[3]                                              
            u[4],  #  dotu[1] = u[4]                                              
            u[5],  #  dotu[2] = u[5]                                              
            2 * omega * u[5] + omega ** 2 * u[0] + n1,  #  dotu[3] = that         
            omega ** 2 * u[1] - 2 * omega * u[4] + n2,  #  dotu[4] = that         
            0]  #  dotu[5] = 0                                                    


dt = np.arange(0.0, 250000.0, .1)
u = odeint(deriv, u0, dt)
x, y, z, x2, y2, z2 = u.T

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x, y, z)
plt.show()
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1 回答 1

2

假设你的意思是这个错误：

~/coding$ python orbit1.py 
Traceback (most recent call last):
  File "orbit1.py", line 61, in <module>
    u = odeint(deriv, u0, dt)
TypeError: 'module' object is not callable

这是因为您想要在 中命名的函数。你的线路odeintscipy.integrate

import scipy.integrate as odeint

导入整个模块并为其命名odeint。尝试

from scipy.integrate import odeint

相反，或

import scipy.integrate
[...]

u = scipy.integrate.odeint(deriv, u0, dt)

这应该给你 在此处输入图像描述

于 2013-04-22T18:03:43.547 回答